Why the Name “Jesus”?

This morning we look at the angel’s command to Joseph about the name of the child the Virgin Mary was carrying: “You are to give him the name Jesus, because he will save his people from their sins.” At what point do you experience being “saved” from your sins? And what is it, regarding sin, that you are saved from? Is it something we can know and enjoy in this life or is it only for the next life? God was very specific in the choice of His incarnate name: JESUS. Why?